Mathematics Colloquium

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Two Problems in Biofluid Mechanics

Speaker: Yoichiro Mori, University of Pennsylvania

Location: Warren Weaver Hall 1302

Date: Monday, April 20, 2026, 3:45 p.m.

Synopsis:

We will discuss two problems in biofluid mechanics. We first discuss open membrane problems. Cells are often breached, resulting in open membranes with edges. We formulate a mathematical model in which a 2D fluid membrane with bending stiffness is immersed in a 3D Stokes fluid. At the 1D edge are imposed the force balance condition from line tension and the torque free condition. We will present numerical simulations for the axisymmetric and planar cases for this problem. The 1D edge results in an inverse square root singularity, necessitating careful numerical treatment. We will then present a preliminary application of our algorithm to the problem of parasite egress from a host cell. Next, we discuss passive tracer dynamics.  We consider the problem of approximating the Langevin dynamics of inertial particles being transported by a background flow using an acceleration corrected advection-diffusion equation. After motivating this approximation, we will discuss finite-time error estimates between the two models when the dimensionless relaxation timescale is small, and present numerical evidence suggesting that this approximation also captures the long-time behavior of the inertial Langevin dynamics.